A374155 a(n) is the least prime that is a quadratic residue modulo prime(n). First column of A373751.

2, 3, 5, 2, 3, 3, 2, 5, 2, 5, 2, 3, 2, 11, 2, 7, 3, 3, 17, 2, 2, 2, 3, 2, 2, 5, 2, 3, 3, 2, 2, 3, 2, 5, 5, 2, 3, 41, 2, 13, 3, 3, 2, 2, 7, 2, 5, 2, 3, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 17, 7, 2, 2, 7, 5, 2, 3, 3, 2, 2, 2, 3, 5, 2, 5, 3, 2, 2, 3, 3, 2, 2, 2

Offset

1,1

Links

Table of n, a(n) for n=1..85.

Example

a(38) = 41 because row 38 of A373751 starts 41, 43, 47, ..., which are the primes that are quadratic residues modulo 163.

Maple

a := proc(n) local a, p; a := 1; p := ithprime(n); while true do a := a + 1;
if NumberTheory:-QuadraticResidue(a, p) = 1 and isprime(a) then return a fi od end: seq(a(n), n = 1..85);

Prog

(PARI) a(n) = my(p=prime(n), q=2); while (!issquare(Mod(q, p)), q=nextprime(q+1)); q; \\ Michel Marcus, Jun 29 2024

Crossrefs

Variant: A306530 (differs in the first 3 values).

Cf. A373751.

Sequence in context: A133907 A232931 A060084 * A361503 A265668 A273087

Adjacent sequences: A374152 A374153 A374154 * A374156 A374157 A374158

Keyword

nonn

Author

Peter Luschny, Jun 29 2024

Status

approved